Speech is expressive in ways that caption text does not capture, with emotion or emphasis information not conveyed. We interviewed eight Deaf and Hard-of-Hearing (dhh) individuals to understand if and how captions' inexpressiveness impacts them in online meetings with hearing peers. Automatically captioned speech, we found, lacks affective depth, lending it a hard-to-parse ambiguity and general dullness. Interviewees regularly feel excluded, which some understand is an inherent quality of these types of meetings rather than a consequence of current caption text design. Next, we developed three novel captioning models that depicted, beyond words, features from prosody, emotions, and a mix of both. In an empirical study, 16 dhh participants compared these models with conventional captions. The emotion-based model outperformed traditional captions in depicting emotions and emphasis, with only a moderate loss in legibility, suggesting its potential as a more inclusive design for captions.